The extra amount that Tim is expected to pay is approximately given by: Option D: $57.88
How to form mathematical expression from the given description?You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
For this case, the question is missing the fact that the size of the tank is 11.75 gallon and a gallon of gas costs $4.50.
So, the total cost of 11.75 gallon of gas is:
Cost of 11.75 gallon gas = 11.75 * 4.50 = 52.875 (in dollars)
Also from the question, the cost of refueling a vehicle is $5.00.
So, the total cost for refueling the car of Tim is:
Total cost = cost of gas + cost of refueling the car
Total cost = 52.875 + 5.00
Total cost = $57.875 ≈ $57.88
Thus, the extra amount that Tim is expected to pay is approximately given by: Option D; $57.88
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1. A quadratic function fis defined by f(x) = (x - 7)(x + 3).
a. Without graphing, identify the x-intercepts of the graph of f. ( , ) and ( , )
b. If x=___, then (____- 7) = 0. If x = ____, then (____+ 3) = 0
c. Expand (x - 7)(x + 3) and use the expanded form to identify the y-intercept of the graph of f. Show work
Expanded form f (x) =_______
y-intercept ( , )
Answer:
a) (-3, 0) and (7, 0)
b) If x = 7 then (7 - 7) = 0
If x = -3 then (-3 + 3) = 0
c) f(x) = x² - 4x - 21
y-intercept (0, -21)
Step-by-step explanation:
a)
x-intercepts are when f(x) = 0
Therefore, if f(x) = (x - 7)(x + 3) then (x - 7)(x + 3) = 0
⇒ x - 7 = 0
⇒ x = 7
and
⇒ x + 3 = 0
⇒ x = -3
So x-intercepts are (-3, 0) and (7, 0)
b) If x = 7 then (7 - 7) = 0
If x = -3 then (-3 + 3) = 0
c) Expand f(x) = (x - 7)(x + 3)
⇒ f(x) = x² + 3x - 7x - 21
⇒ f(x) = x² - 4x - 21
The y-intercept is when x = 0 ⇒ (0, -21)
Which expression has the same meaning as n 3/8?
Answer:
I think its the one on the bottom right
Step-by-step explanation:
Answer:
bottom right is the answer i think
What is the value of x?
102°
xº
O 51
O 102
O 12
O 78
Answer:
102(vertically opposite angle)
9y-2y+8=4y+38 answer
Answer: y = 10
Step-by-step explanation: Hi there!
To get started, first, we have to subtract 2y from 9y on the left side.
7y + 8 = 4y + 38
Then subtract 4y on both sides.
3y + 8 = 38
Then subtract 8 on both sides
3y = 30
Finally divide by 3 on both sides.
y = 10
The answer is y = 10.
Answer: y=10
Step-by-step explanation:
9y-2y+8=4y+38
[tex]\mathrm{Add\:similar\:elements:}\:9y-2y=7y[/tex]
7y+8=4y+38
[tex]\mathrm{Subtract\:}8\mathrm{\:from\:both\:sides}[/tex]
7y+8-8=4y+38-8
[tex]\mathrm{Simplify}[/tex]
7y=4y+30
[tex]\mathrm{Subtract\:}4y\mathrm{\:from\:both\:sides}[/tex]
7y-4y=4y+30-4y
[tex]\mathrm{Simplify}[/tex]
3y=30
[tex]\mathrm{Divide\:both\:sides\:by\:}3[/tex]
[tex]\frac{3y}{3}=\frac{30}{3}[/tex]
Simplify
y=10
how do you graph y=-4/3x+1
Answer:
Step-by-step explanation:
Answer:
Hope this helps any!
Step-by-step explanation:
A car dealership paid $9,000 for a car. The sticker price is $10,395 for a customer to buy the car. a. What’s the markup in dollars? b. By what percent is the markup?
Answer:
1) To determine how much the change of $9,000 to $10,395, we must subtract 9,000 from 10,395;
10,395 - 9,000 = $1,395 is the change in price (an increase).
Formula to find percentage of change;
Change in price/original amount x 100% (100/100)
Replace those values:
1,935 (change in price/increase) 100
_____ x _____ = %0.215
9,000(original amount) 100
Suppose y varies directly as x, and y = 10 when x = 25. Find y when x = 18.
Answer:
y = 7.2
Step-by-step explanation:
Given that y varies directly as x then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition y = 10 when x = 25, then
10 = 25k ( divide both sides by 25 )
[tex]\frac{10}{25}[/tex] = 0.4 = k
y = 0.4x ← equation of variation
When x = 18, then
y = 0.4 × 18 = 7.2
okays here's the question
Answer:
12
Step-by-step explanation:
What property can solve 2x-2+2=12+2
Answer:
7Step-by-step explanation:
2x-2+2=12+2
= 2x+0=14
= 2x=14
= X=14÷2
= X=7
Thank you ☺️☺️☺️☺️
Use the long division method to find the result when 6x^2 + 26x^2 + 23x + 5 is divided by 3x + 1. explain all steps
Dividing 6x^2 + 26x^2 + 23x + 5 by 3x + 1 using the long division involves the use of groups or parts
The result when 6x^2 + 26x^2 + 23x + 5 is divided by 3x + 1 is 2x^2 + 8x + 5 with no remainder
How to carry out the long division?The dividend is given as:
6x^2 + 26x^2 + 23x + 5
And the divisor is 3x + 1
Step 1:Divide 6x^3 by 3x:
Result = 2x^2
Multiply 2x^2 by 3x + 1
=> 6x^3 + 2x^2
Subtract 6x^3 + 2x^2 from 6x^3 + 26x^2 + 23x + 5
=> 24x^2 + 23x + 5
Step 2:Divide 24x^2 by 3x:
Result = 8x
Multiply 8x by 3x + 1
=> 24x^2 + 8x
Subtract 24x^2 + 8x from 24x^2 + 23x + 5
=> 15x + 5
Step 3:Divide 15x by 3x:
Result = 5
Multiply 5 by 3x + 1
=> 15x + 5
Subtract 15x + 5 from 15x + 5
=> 0
Write out the sum of the results
Result = 2x^2 + 8x + 5
Hence, the result when 6x^2 + 26x^2 + 23x + 5 is divided by 3x + 1 is 2x^2 + 8x + 5 with no remainder
See attachment for the long division process
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500g to 2kg in fraction
Answer:
1∶ 4
explanation
What are the FACTORS in this equation:
3 x 4 = 12
Answer:
3 &4
Step-by-step explanation:
Factor is something that is being multiplied together.
Finding an angle measure given extended triangles
Check the picture below.
What is the standard deviation of the data set? 1, 4, 2, 2, 8, 7, 3 Round your answer to the nearest tenth.
Standard deviation is a measurement of a collection of values' variance or dispersion. The standard deviation of the data set is 2.474.
How to calculate the standard deviation of a data set?Step 1: Find the mean
Step 2: Find each score’s deviation from the mean
Step 3: Square each deviation from the mean
Step 4: Find the sum of squares
Step 5: Apply the formula
[tex]SD = \sqrt{\dfrac{\sum(x_i-\bar{x})^2}{n}}[/tex]
The data set that is given to us is {1, 4, 2, 2, 8, 7, 3}, now use the steps to calculate the standard deviation.
Step 1: Find the mean
The mean of the given data set can be written as,
[tex]Mean, \mu=\dfrac{1+4+2+2+8+7+3}{7} = 3.857[/tex]
Step 2: Find each score’s deviation from the mean
1 - 3.857 = -2.857
4 - 3.857 = 0.143
2 - 3.857= -1.857
2 - 3.857= -1.857
8 - 3.857 = 4.143
7 - 3.857 = 3.143
3 - 3.857 = -0.857
Step 3: Square each deviation from the mean
-2.857² = 8.162
0.143² = 0.02
-1.857² = 3.447
-1.857² = 3.447
4.143² = 17.165
3.143² = 9.877
-0.857²= 0.735
Step 4: Find the sum of squares
8.162+0.20+3.447+3.447+17.165+9.877+0.735 = 42.857
Step 5: Apply the formula
[tex]SD = \sqrt{\dfrac{\sum(x_i-\bar{x})^2}{n}}\\\\SD = \sqrt{\dfrac{42.857}{7}} \\\\SD= 2.474[/tex]
Hence, the standard deviation of the data set is 2.474.
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Someone please help me on this I’m stuck
A store offers a loan for $900 to buy a computer. The terms of the loan
are for 9% simple interest and equal monthly payments for three years.
What is the monthly payment?
O $1143
O $700
o $31.75
o $92.50
Answer:
(c) $31.75
Step-by-step explanation:
First of all, you need to use some number sense to estimate an answer.
If the $900 loan had no interest, 1/3 of it would be paid off in each of the 3 years, or about $300 each year. You will be making 12 monthly payments each year, so the amount of principal being paid with each payment is $300/12 = $25. Any answer much above this amount will not make sense, so you can immediately reject all choices except $31.75.
__
The simple interest on the loan is ...
I = Prt = $900×0.09×3 = $243
That, too, is divided among the 36 payments, so adds ...
$243/36 = $6.75 to each of the $25 payments we calculated above.
The monthly payment is ...
$25 +6.75 = $31.75
The prism shown has a volume of 35cm³
Work out h, the height of the triangular cross section.
Answer:
h = 2.5 cm
Step-by-step explanation:
the volume (V) of a prism is calculated as
V = Al ( A is the area of triangular base and l the length )
A = [tex]\frac{1}{2}[/tex] bh = [tex]\frac{1}{2}[/tex] × 4 × h = 2h and l = 7
given V = 35 , then
2h × 7 = 35
14h = 35 ( divide both sides by 14 )
h = 2.5 cm
The diameter of a cylinder is 3 yd. The height is 8 yd. What is the volume of a cylinder ( put the answer in yd)
Answer:
18[tex]\pi[/tex] yd.³ or 56.54867 yd.³
Step-by-step explanation:
The volume of a cylinder can be written as: height × base, where the base of the cylinder is [tex]\pi[/tex]r².
Since the radius (r) is half the diameter, it should be 1.5 or 3/2 yd.
r = 1.5
So, the area of the base of the cylinder is 1.5²([tex]\pi[/tex]), which is equal to 2.25[tex]\pi[/tex].
Now multiply that by the height, 8 yd.
2.25[tex]\pi[/tex] × 8 = 18[tex]\pi[/tex]
The area of the cylinder is 18[tex]\pi[/tex] or 56.54867
Answer:
56.55 yd.³ OR 56.52 yd.³
Step-by-step explanation:
The formula for the volume of a cylinder is; V=πr^2h
To find the volume let's put in the values they gave us.
Now: V=π times 1.5^2 times 8
(If you don't know what pi or π is its the area of a unit circle. So the area of a circle with diameter 2 or radius 1)
Continuing the volume would be 3.141592.. * 2.25 * 8 ( '*' indicates multiplication) Now the answer after you multiply would be approx. 56.54867 which rounded would be 56.55
NOW if your teacher prefers to use 22/7 or 3.14 as pi then here is your answer:V=πr^2h so 3.14*2.25*8 which would be 56.52 yd.³ (if this is the way you need it ignore ANY other answers)
Alexis is drawing jolly ranchers from two bags the fist bag has 4 red 2 green and one blue the second bag has 4 red and 2 orange what is the probability that he would choose a purple jolly rancher from the first bag and a red jolly rancher from the second
Answer and explanation:
The two events of choosing jolly ranchers from each bag, first and second are independent events so the probability of first event AND second event will be multiplied
First bag has 4 red 2 green and one blue
Second bag has 4 red and 2 orange
what is the probability that he would choose a purple jolly rancher from the first bag and a red jolly rancher from the second
Probability = number of favourable outcomes /total number of favourable outcomes
The first bag does not have a purple jolly rancher and so probability is zero
the second bag's probability of choosing a red jolly rancher =4/6
probability of choosing a purple jolly rancher from first bag and red jolly rancher from second bag
=0*4/6=0
Answer=0
Decrease £16855.21 by 13.5%
Give your answer rounded to 2 DP.
Answer:
14,579.76
Step-by-step explanation:
New value =
16,855.21 - Percentage decrease =
16,855.21 - (13.5% × 16,855.21) =
16,855.21 - 13.5% × 16,855.21 =
(1 - 13.5%) × 16,855.21 =
(100% - 13.5%) × 16,855.21 =
86.5% × 16,855.21 =
86.5 ÷ 100 × 16,855.21 =
86.5 × 16,855.21 ÷ 100 =
1,457,975.665 ÷ 100 =
14,579.75665 ≈
14,579.76
1/2 times -1/4 PLEASEEEEEE
Answer:-0.125 or 1/8
Step-by-step explanation: :)
Answer:
-1/8
Step-by-step explanation:
1/2 times -1/4 = -1/8
Find the volume of this object use 3 for pi
Answer:
The volume of the circle is 21
Step-by-step explanation:
The volume of rectangular is 60
the first one will get the brianlist please help answer these two
Answer:
Hello bakugo here!
Step-by-step explanation:
I don't see anything, is there supposed to be anything here? if not
Thank you extra for FREE points! :D
What value of x is in the solution set of 2x - 3> 11 - 5x?
A. -3
B. 0
C. 2
D. 4
Answer:
The answer is D : 4.
Step-by-step explanation:
=2x-3>11-5x
=2x-3+5x>11
=7x-3>11
=7x>11+3
=7x>14
=7x/7>14/7
=x>2
By simplifying the problem, you can see that "x" must be greater than 2. Therefore, eliminating all other possible answers that are shown, but 4.
I answered the same questions with the same exact wording and explanation so please don't report any answers that are the same as this one, they are all mine and written by me.
Please someone help me solve c no.
Answer:
Step-by-step explanation:
Dilate the figure below with a scale factor of 1.5 centered at the origin and then rotate the figure 90° clockwise about the origin.
Answer:
Step-by-step explanation:
Vertices of the quadrilateral are (-4, 1), (-3, 2), (-1, 2) and (-2, 1).
If the given quadrilateral is dilated by ta scale factor of 1.5 about the origin.
Rule for the dilation,
(x, y) → (kx, ky) [k = scale factor]
New vertices of the quadrilateral after the transformation will be,
(-4, 1) → (1.5×4, 1.5×1)
→ (-6, 1.5)
(-3, 2) → (-4.5, 3)
(-1, 2) → (-1.5, 3)
(-2, 1) → (-3, 1.5)
Now the new points are rotated by 90° clockwise about the origin,
Rule for the rotation of the points,
(x, y) → (y, -x)
So the new vertices will be,
(-6, 1.5) → (1.5, 6)
(-4.5, 3) → (3, 4.5)
(-1.5, 3) → (3, 1.5)
(-3, 1.5) → (1.5, 3)
We can plot these points on the graph to form a new (image) quadrilateral.
Trina is saving to buy a new phone. She has two options. The first option is to put $400 away initially and save $20 every month. The second option is to put $100 away initially and save $40 every month. After how many months, m, would Trina save the same amount using either option? How much would she save with either option? Write and solve an equation to show your work.
Total amount saved in 1st case :
[tex]S_1=400+20t_1[/tex]
Total amount saved in 2nd case :
[tex]S_2=100+40t_2[/tex]
( Here [tex]t_1 \ and\ t_2[/tex] are number of months )
Let, after x months the amount saved in both cases is same.
So,
[tex]S_2=S_1\\\\100+40x=400+20x\\\\20x = 300\\\\x = 15\ months[/tex]
Amount saved :
[tex]S_1=400+20(15) =\$ 700[/tex]
[tex]S_2=100+40( 15)= \$700[/tex]
Hence, this is the required solution.
Please solve this equation.
Answer:
1/3
Step-by-step explanation:
5/6 - 1/2
note that you could also write 1/2 as 3/6 since when divided you get half once again .
5/6- 3/6 = (5-3)/6= 2/6 = 1/3
Answer:
The answer is
[tex] \huge \frac{1}{3} [/tex]
Step-by-step explanation:
[tex] \frac{5}{6} - \frac{1}{2} \\ [/tex]
To solve this first find the common denominator
From the question the common denominator is 6
So we have
[tex] \frac{5}{6} - \frac{1}{2} = \frac{5 - 3}{6} = \frac{2}{6} = \frac{1}{3} \\ [/tex]
We have the final answer as
[tex] \frac{1}{3} \\ [/tex]
Hope this helps you
While in transit, the antitoxin had to stay between 36ºF and 46ºF. The dogsled teams stopped along the route often to warm the antitoxin by a fire to prevent it from freezing. A range of how many degrees Fahrenheit was ideal for the antitoxin?
Sarah hit the ball 3 times out of the 8 times. What is the experimental probability (as a percent) that she will hit the ball next? A 22.5% B 37.5% 45% 3% asap
Answer:
B
Step-by-step explanation:
3/8 is equal to 0.375, also known as 37.5%.
The experimental probability (as a percent) that she will hit the ball next is 37.5%. Hence, option B is the right choice.
What do we mean by the experimental probability of an event?The experimental probability of an event occurring is the number of times it happened during the experiment as a ratio to the number of times the experiment was run.
How do we solve the given question?In the question, we are given that Sarah hit the ball 3 times out of the 8 times.
We are asked to find the experimental probability (as a percent) that she will hit the ball next.
As we know, the experimental probability of an event occurring is the number of times it happened during the experiment as a ratio to the number of times the experiment was run.
∴ The experimental probability = The number of times Sarah hit the ball/The number of times she experimented = 3/8
or, The experimental probability = (3/8)*100 % = (3*25)/2 % = 75/2 % = 37.5%.
∴ The experimental probability (as a percent) that she will hit the ball next is 37.5%. Hence, option B is the right choice.
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Sam has sheets of metal which are 36 cm by 36 cm square. He wants to cut out identical squares which are x cm by I cm from the corners of each sheet. He will then bend the sheets along the dashed lines to form an open container. a Show that the volume of the container is given by V(2) = x(36 – 2x)2 cm? . b What sized squares should be cut out to produce the container of greatest capacity? 36 cm 36 cm
Four squares with size of 6 centimeters should be cut to produce the container of greatest capacity.
How to model and analyse an open boxa) The volume of the box ([tex]V[/tex]), in cubic centimeters, is equal to the area of the base ([tex]A[/tex]), in square centimeters, multiplied by the height of the box ([tex]h[/tex]), in centimeters. The area of the surface is the product of the width ([tex]w[/tex]) and length (l), both in centimeters:
[tex]V = w\cdot l\cdot h[/tex]
[tex]V = (36-2\cdot x)^{2}\cdot x[/tex] (1)
The volume of the container is [tex]V = (36-2\cdot x)\cdot x[/tex] cubic centimeters. [tex]\blacksquare[/tex]
b) We need to apply first derivative analysis and second derivative analysis to determine the dimensions of the maximum squares to be cut:
FDT[tex]-4\cdot (36-2\cdot x)\cdot x+(36-2\cdot x)^{2} = 0[/tex]
[tex]-4\cdot x + 36-2\cdot x = 0[/tex]
[tex]6\cdot x = 36[/tex]
[tex]x = 6[/tex]
SDT[tex]V'' (x) = -4\cdot [(-2)\cdot x+(36-2\cdot x)]-4\cdot (36-2\cdot x)\cdot x + (36-2\cdot x)^{2}[/tex]
[tex]V''(x) = 8\cdot x-4\cdot (36-2\cdot x)-4\cdot (36\cdot x-2\cdot x^{2})+(36-2\cdot x)^{2}[/tex]
[tex]V'' (6) = -48[/tex]
Since [tex]V''(6) < 0[/tex], the critical value of [tex]x[/tex] leads to a maximum.
Four squares with size of 6 centimeters should be cut to produce the container of greatest capacity. [tex]\blacksquare[/tex]
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